
import pandas as pd
from sklearn import metrics
from sklearn.metrics import mean_squared_error
from sklearn.preprocessing import StandardScaler
from sklearn.model_selection import  GridSearchCV,KFold, cross_validate
from sklearn.linear_model import ElasticNetCV
import matplotlib
import matplotlib.pyplot as plt
import numpy as np
import cufflinks as cf
import plotly as py
from plotly.offline import download_plotlyjs, init_notebook_mode, plot, iplot
init_notebook_mode(connected=True)
cf.go_offline()
from sklearn.exceptions import ConvergenceWarning
ConvergenceWarning('ignore')
import warnings
warnings.filterwarnings("ignore")


df_train = pd.read_csv(r'/Users/allen/Desktop/MSDS/QTW/qtw_smu/Case Study 1: Linear Regression/superconduct/train.csv')
df_unique_m = pd.read_csv(r'/Users/allen/Desktop/MSDS/QTW/qtw_smu/Case Study 1: Linear Regression/superconduct/unique_m.csv')


#merge two dataframes on indexes
df_merge = pd.merge(df_train, df_unique_m, left_index=True, right_index=True)


#delete duplicate and unused column
df_merge = df_merge.drop(['critical_temp_y','material'], axis=1)

#rename column from merge
df_merge.rename(columns = {'critical_temp_x':'critical_temp'}, inplace = True)


df_merge.head()


#show all columns..
pd.set_option('display.max_columns', None)


df_train.head()


df_unique_m.head()


df_train_shape = df_train.shape
df_unique_m_shape = df_unique_m.shape
df_merge_shape = df_merge.shape
print(f'Train DataFrame Shape: {df_train_shape}')
print(f'Unique_m DataFrame Shape:{df_unique_m_shape}')
print(f'Merged DataFrame Shape:{df_merge_shape}')

Train DataFrame Shape: (21263, 82)
Unique_m DataFrame Shape:(21263, 88)
Merged DataFrame Shape:(21263, 168)


df_train.info(verbose = True)

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 21263 entries, 0 to 21262
Data columns (total 82 columns):
 #   Column                           Non-Null Count  Dtype  
---  ------                           --------------  -----  
 0   number_of_elements               21263 non-null  int64  
 1   mean_atomic_mass                 21263 non-null  float64
 2   wtd_mean_atomic_mass             21263 non-null  float64
 3   gmean_atomic_mass                21263 non-null  float64
 4   wtd_gmean_atomic_mass            21263 non-null  float64
 5   entropy_atomic_mass              21263 non-null  float64
 6   wtd_entropy_atomic_mass          21263 non-null  float64
 7   range_atomic_mass                21263 non-null  float64
 8   wtd_range_atomic_mass            21263 non-null  float64
 9   std_atomic_mass                  21263 non-null  float64
 10  wtd_std_atomic_mass              21263 non-null  float64
 11  mean_fie                         21263 non-null  float64
 12  wtd_mean_fie                     21263 non-null  float64
 13  gmean_fie                        21263 non-null  float64
 14  wtd_gmean_fie                    21263 non-null  float64
 15  entropy_fie                      21263 non-null  float64
 16  wtd_entropy_fie                  21263 non-null  float64
 17  range_fie                        21263 non-null  float64
 18  wtd_range_fie                    21263 non-null  float64
 19  std_fie                          21263 non-null  float64
 20  wtd_std_fie                      21263 non-null  float64
 21  mean_atomic_radius               21263 non-null  float64
 22  wtd_mean_atomic_radius           21263 non-null  float64
 23  gmean_atomic_radius              21263 non-null  float64
 24  wtd_gmean_atomic_radius          21263 non-null  float64
 25  entropy_atomic_radius            21263 non-null  float64
 26  wtd_entropy_atomic_radius        21263 non-null  float64
 27  range_atomic_radius              21263 non-null  int64  
 28  wtd_range_atomic_radius          21263 non-null  float64
 29  std_atomic_radius                21263 non-null  float64
 30  wtd_std_atomic_radius            21263 non-null  float64
 31  mean_Density                     21263 non-null  float64
 32  wtd_mean_Density                 21263 non-null  float64
 33  gmean_Density                    21263 non-null  float64
 34  wtd_gmean_Density                21263 non-null  float64
 35  entropy_Density                  21263 non-null  float64
 36  wtd_entropy_Density              21263 non-null  float64
 37  range_Density                    21263 non-null  float64
 38  wtd_range_Density                21263 non-null  float64
 39  std_Density                      21263 non-null  float64
 40  wtd_std_Density                  21263 non-null  float64
 41  mean_ElectronAffinity            21263 non-null  float64
 42  wtd_mean_ElectronAffinity        21263 non-null  float64
 43  gmean_ElectronAffinity           21263 non-null  float64
 44  wtd_gmean_ElectronAffinity       21263 non-null  float64
 45  entropy_ElectronAffinity         21263 non-null  float64
 46  wtd_entropy_ElectronAffinity     21263 non-null  float64
 47  range_ElectronAffinity           21263 non-null  float64
 48  wtd_range_ElectronAffinity       21263 non-null  float64
 49  std_ElectronAffinity             21263 non-null  float64
 50  wtd_std_ElectronAffinity         21263 non-null  float64
 51  mean_FusionHeat                  21263 non-null  float64
 52  wtd_mean_FusionHeat              21263 non-null  float64
 53  gmean_FusionHeat                 21263 non-null  float64
 54  wtd_gmean_FusionHeat             21263 non-null  float64
 55  entropy_FusionHeat               21263 non-null  float64
 56  wtd_entropy_FusionHeat           21263 non-null  float64
 57  range_FusionHeat                 21263 non-null  float64
 58  wtd_range_FusionHeat             21263 non-null  float64
 59  std_FusionHeat                   21263 non-null  float64
 60  wtd_std_FusionHeat               21263 non-null  float64
 61  mean_ThermalConductivity         21263 non-null  float64
 62  wtd_mean_ThermalConductivity     21263 non-null  float64
 63  gmean_ThermalConductivity        21263 non-null  float64
 64  wtd_gmean_ThermalConductivity    21263 non-null  float64
 65  entropy_ThermalConductivity      21263 non-null  float64
 66  wtd_entropy_ThermalConductivity  21263 non-null  float64
 67  range_ThermalConductivity        21263 non-null  float64
 68  wtd_range_ThermalConductivity    21263 non-null  float64
 69  std_ThermalConductivity          21263 non-null  float64
 70  wtd_std_ThermalConductivity      21263 non-null  float64
 71  mean_Valence                     21263 non-null  float64
 72  wtd_mean_Valence                 21263 non-null  float64
 73  gmean_Valence                    21263 non-null  float64
 74  wtd_gmean_Valence                21263 non-null  float64
 75  entropy_Valence                  21263 non-null  float64
 76  wtd_entropy_Valence              21263 non-null  float64
 77  range_Valence                    21263 non-null  int64  
 78  wtd_range_Valence                21263 non-null  float64
 79  std_Valence                      21263 non-null  float64
 80  wtd_std_Valence                  21263 non-null  float64
 81  critical_temp                    21263 non-null  float64
dtypes: float64(79), int64(3)
memory usage: 13.3 MB


df_unique_m.info(verbose = True)

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 21263 entries, 0 to 21262
Data columns (total 88 columns):
 #   Column         Non-Null Count  Dtype  
---  ------         --------------  -----  
 0   H              21263 non-null  float64
 1   He             21263 non-null  int64  
 2   Li             21263 non-null  float64
 3   Be             21263 non-null  float64
 4   B              21263 non-null  float64
 5   C              21263 non-null  float64
 6   N              21263 non-null  float64
 7   O              21263 non-null  float64
 8   F              21263 non-null  float64
 9   Ne             21263 non-null  int64  
 10  Na             21263 non-null  float64
 11  Mg             21263 non-null  float64
 12  Al             21263 non-null  float64
 13  Si             21263 non-null  float64
 14  P              21263 non-null  float64
 15  S              21263 non-null  float64
 16  Cl             21263 non-null  float64
 17  Ar             21263 non-null  int64  
 18  K              21263 non-null  float64
 19  Ca             21263 non-null  float64
 20  Sc             21263 non-null  float64
 21  Ti             21263 non-null  float64
 22  V              21263 non-null  float64
 23  Cr             21263 non-null  float64
 24  Mn             21263 non-null  float64
 25  Fe             21263 non-null  float64
 26  Co             21263 non-null  float64
 27  Ni             21263 non-null  float64
 28  Cu             21263 non-null  float64
 29  Zn             21263 non-null  float64
 30  Ga             21263 non-null  float64
 31  Ge             21263 non-null  float64
 32  As             21263 non-null  float64
 33  Se             21263 non-null  float64
 34  Br             21263 non-null  float64
 35  Kr             21263 non-null  int64  
 36  Rb             21263 non-null  float64
 37  Sr             21263 non-null  float64
 38  Y              21263 non-null  float64
 39  Zr             21263 non-null  float64
 40  Nb             21263 non-null  float64
 41  Mo             21263 non-null  float64
 42  Tc             21263 non-null  float64
 43  Ru             21263 non-null  float64
 44  Rh             21263 non-null  float64
 45  Pd             21263 non-null  float64
 46  Ag             21263 non-null  float64
 47  Cd             21263 non-null  float64
 48  In             21263 non-null  float64
 49  Sn             21263 non-null  float64
 50  Sb             21263 non-null  float64
 51  Te             21263 non-null  float64
 52  I              21263 non-null  float64
 53  Xe             21263 non-null  int64  
 54  Cs             21263 non-null  float64
 55  Ba             21263 non-null  float64
 56  La             21263 non-null  float64
 57  Ce             21263 non-null  float64
 58  Pr             21263 non-null  float64
 59  Nd             21263 non-null  float64
 60  Pm             21263 non-null  int64  
 61  Sm             21263 non-null  float64
 62  Eu             21263 non-null  float64
 63  Gd             21263 non-null  float64
 64  Tb             21263 non-null  float64
 65  Dy             21263 non-null  float64
 66  Ho             21263 non-null  float64
 67  Er             21263 non-null  float64
 68  Tm             21263 non-null  float64
 69  Yb             21263 non-null  float64
 70  Lu             21263 non-null  float64
 71  Hf             21263 non-null  float64
 72  Ta             21263 non-null  float64
 73  W              21263 non-null  float64
 74  Re             21263 non-null  float64
 75  Os             21263 non-null  float64
 76  Ir             21263 non-null  float64
 77  Pt             21263 non-null  float64
 78  Au             21263 non-null  float64
 79  Hg             21263 non-null  float64
 80  Tl             21263 non-null  float64
 81  Pb             21263 non-null  float64
 82  Bi             21263 non-null  float64
 83  Po             21263 non-null  int64  
 84  At             21263 non-null  int64  
 85  Rn             21263 non-null  int64  
 86  critical_temp  21263 non-null  float64
 87  material       21263 non-null  object 
dtypes: float64(78), int64(9), object(1)
memory usage: 14.3+ MB


df_merge.info(verbose = True)

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 21263 entries, 0 to 21262
Data columns (total 168 columns):
 #    Column                           Dtype  
---   ------                           -----  
 0    number_of_elements               int64  
 1    mean_atomic_mass                 float64
 2    wtd_mean_atomic_mass             float64
 3    gmean_atomic_mass                float64
 4    wtd_gmean_atomic_mass            float64
 5    entropy_atomic_mass              float64
 6    wtd_entropy_atomic_mass          float64
 7    range_atomic_mass                float64
 8    wtd_range_atomic_mass            float64
 9    std_atomic_mass                  float64
 10   wtd_std_atomic_mass              float64
 11   mean_fie                         float64
 12   wtd_mean_fie                     float64
 13   gmean_fie                        float64
 14   wtd_gmean_fie                    float64
 15   entropy_fie                      float64
 16   wtd_entropy_fie                  float64
 17   range_fie                        float64
 18   wtd_range_fie                    float64
 19   std_fie                          float64
 20   wtd_std_fie                      float64
 21   mean_atomic_radius               float64
 22   wtd_mean_atomic_radius           float64
 23   gmean_atomic_radius              float64
 24   wtd_gmean_atomic_radius          float64
 25   entropy_atomic_radius            float64
 26   wtd_entropy_atomic_radius        float64
 27   range_atomic_radius              int64  
 28   wtd_range_atomic_radius          float64
 29   std_atomic_radius                float64
 30   wtd_std_atomic_radius            float64
 31   mean_Density                     float64
 32   wtd_mean_Density                 float64
 33   gmean_Density                    float64
 34   wtd_gmean_Density                float64
 35   entropy_Density                  float64
 36   wtd_entropy_Density              float64
 37   range_Density                    float64
 38   wtd_range_Density                float64
 39   std_Density                      float64
 40   wtd_std_Density                  float64
 41   mean_ElectronAffinity            float64
 42   wtd_mean_ElectronAffinity        float64
 43   gmean_ElectronAffinity           float64
 44   wtd_gmean_ElectronAffinity       float64
 45   entropy_ElectronAffinity         float64
 46   wtd_entropy_ElectronAffinity     float64
 47   range_ElectronAffinity           float64
 48   wtd_range_ElectronAffinity       float64
 49   std_ElectronAffinity             float64
 50   wtd_std_ElectronAffinity         float64
 51   mean_FusionHeat                  float64
 52   wtd_mean_FusionHeat              float64
 53   gmean_FusionHeat                 float64
 54   wtd_gmean_FusionHeat             float64
 55   entropy_FusionHeat               float64
 56   wtd_entropy_FusionHeat           float64
 57   range_FusionHeat                 float64
 58   wtd_range_FusionHeat             float64
 59   std_FusionHeat                   float64
 60   wtd_std_FusionHeat               float64
 61   mean_ThermalConductivity         float64
 62   wtd_mean_ThermalConductivity     float64
 63   gmean_ThermalConductivity        float64
 64   wtd_gmean_ThermalConductivity    float64
 65   entropy_ThermalConductivity      float64
 66   wtd_entropy_ThermalConductivity  float64
 67   range_ThermalConductivity        float64
 68   wtd_range_ThermalConductivity    float64
 69   std_ThermalConductivity          float64
 70   wtd_std_ThermalConductivity      float64
 71   mean_Valence                     float64
 72   wtd_mean_Valence                 float64
 73   gmean_Valence                    float64
 74   wtd_gmean_Valence                float64
 75   entropy_Valence                  float64
 76   wtd_entropy_Valence              float64
 77   range_Valence                    int64  
 78   wtd_range_Valence                float64
 79   std_Valence                      float64
 80   wtd_std_Valence                  float64
 81   critical_temp                    float64
 82   H                                float64
 83   He                               int64  
 84   Li                               float64
 85   Be                               float64
 86   B                                float64
 87   C                                float64
 88   N                                float64
 89   O                                float64
 90   F                                float64
 91   Ne                               int64  
 92   Na                               float64
 93   Mg                               float64
 94   Al                               float64
 95   Si                               float64
 96   P                                float64
 97   S                                float64
 98   Cl                               float64
 99   Ar                               int64  
 100  K                                float64
 101  Ca                               float64
 102  Sc                               float64
 103  Ti                               float64
 104  V                                float64
 105  Cr                               float64
 106  Mn                               float64
 107  Fe                               float64
 108  Co                               float64
 109  Ni                               float64
 110  Cu                               float64
 111  Zn                               float64
 112  Ga                               float64
 113  Ge                               float64
 114  As                               float64
 115  Se                               float64
 116  Br                               float64
 117  Kr                               int64  
 118  Rb                               float64
 119  Sr                               float64
 120  Y                                float64
 121  Zr                               float64
 122  Nb                               float64
 123  Mo                               float64
 124  Tc                               float64
 125  Ru                               float64
 126  Rh                               float64
 127  Pd                               float64
 128  Ag                               float64
 129  Cd                               float64
 130  In                               float64
 131  Sn                               float64
 132  Sb                               float64
 133  Te                               float64
 134  I                                float64
 135  Xe                               int64  
 136  Cs                               float64
 137  Ba                               float64
 138  La                               float64
 139  Ce                               float64
 140  Pr                               float64
 141  Nd                               float64
 142  Pm                               int64  
 143  Sm                               float64
 144  Eu                               float64
 145  Gd                               float64
 146  Tb                               float64
 147  Dy                               float64
 148  Ho                               float64
 149  Er                               float64
 150  Tm                               float64
 151  Yb                               float64
 152  Lu                               float64
 153  Hf                               float64
 154  Ta                               float64
 155  W                                float64
 156  Re                               float64
 157  Os                               float64
 158  Ir                               float64
 159  Pt                               float64
 160  Au                               float64
 161  Hg                               float64
 162  Tl                               float64
 163  Pb                               float64
 164  Bi                               float64
 165  Po                               int64  
 166  At                               int64  
 167  Rn                               int64  
dtypes: float64(156), int64(12)
memory usage: 27.3 MB


df_merge.describe()


df_merge['critical_temp'].iplot(
    kind='hist',
    bins=100,
    xTitle='Critical Temperature',
    linecolor='black',
    yTitle='count',
    title='Histogram of Critical Temperature')


scatter_cols = ['number_of_elements','mean_atomic_mass','mean_atomic_radius','critical_temp']
df_scatter = df_merge[scatter_cols]
df_scatter.scatter_matrix()


# Subset of columns to transform
scale_cols = df_merge.columns[df_merge.columns != 'critical_temp']

# Scale Columns
sc = StandardScaler()
df_merge[scale_cols] = sc.fit_transform(df_merge[scale_cols])


#Specififying Stratified Kfold for cv.
kfcv = KFold(n_splits=10,random_state=0,shuffle=True)


#Set target and feature columns
target_col = ['critical_temp']
feature_cols = df_merge.loc[:, ~df_merge.columns.isin(target_col)].columns
y = df_merge.critical_temp
X = df_merge[feature_cols]


%%time
# Grid search for Linear Regression task 1

lr_grid={"l1_ratio":np.arange(0.0,1.0,0.1), 
      "tol": [1e-9,1e-8,1e-7,1e-6,1e-5, 1e-4, 1e-3, 1e-2, 1e-1],
      "eps":[1e-3, 1e-2, 1e-1,1,10,100]
      }

model=ElasticNetCV(random_state = 0,max_iter=10000)

model_gs=GridSearchCV(model,
                       lr_grid,
                       cv = kfcv,
                       n_jobs=-1,
                       scoring = "neg_root_mean_squared_error")

model_gs.fit(X,y)
best_params = model_gs.best_params_
print(f'Grid Search Best Parameters{best_params}')

Grid Search Best Parameters{'eps': 0.001, 'l1_ratio': 0.5, 'tol': 0.1}
CPU times: user 11 s, sys: 5.65 s, total: 16.7 s
Wall time: 9min 58s


model_ = ElasticNetCV(l1_ratio =.5 ,
                        tol =0.1,
                        eps =0.001,
                        random_state = 0,
                        max_iter = 10000)

model_score = cross_validate(model_, X, y,
                            scoring='neg_root_mean_squared_error',
                            cv=kfcv,
                            return_estimator=True,
                            n_jobs=-1,
                            return_train_score=True)

model_results = pd.DataFrame(model_score)
model_results.loc['mean'] = model_results.mean()
print(model_results.to_markdown())

|      |   fit_time |   score_time | estimator                                             |   test_score |   train_score |
|:-----|-----------:|-------------:|:------------------------------------------------------|-------------:|--------------:|
| 0    |   0.790638 |   0.00162292 | ElasticNetCV(max_iter=10000, random_state=0, tol=0.1) |     -17.8198 |      -17.6992 |
| 1    |   0.790282 |   0.00154591 | ElasticNetCV(max_iter=10000, random_state=0, tol=0.1) |     -19.5118 |      -17.4999 |
| 2    |   0.767968 |   0.00222802 | ElasticNetCV(max_iter=10000, random_state=0, tol=0.1) |     -17.8285 |      -17.6565 |
| 3    |   0.786807 |   0.00218701 | ElasticNetCV(max_iter=10000, random_state=0, tol=0.1) |     -17.6732 |      -17.6302 |
| 4    |   0.754597 |   0.00209999 | ElasticNetCV(max_iter=10000, random_state=0, tol=0.1) |     -17.8176 |      -17.703  |
| 5    |   0.784165 |   0.0020647  | ElasticNetCV(max_iter=10000, random_state=0, tol=0.1) |     -17.1766 |      -17.7352 |
| 6    |   0.762796 |   0.0016861  | ElasticNetCV(max_iter=10000, random_state=0, tol=0.1) |     -17.8488 |      -17.7298 |
| 7    |   0.778274 |   0.0014472  | ElasticNetCV(max_iter=10000, random_state=0, tol=0.1) |     -18.0257 |      -17.6453 |
| 8    |   0.762333 |   0.00171614 | ElasticNetCV(max_iter=10000, random_state=0, tol=0.1) |     -17.7077 |      -17.629  |
| 9    |   0.74049  |   0.00208688 | ElasticNetCV(max_iter=10000, random_state=0, tol=0.1) |     -17.8841 |      -17.6424 |
| mean |   0.771835 |   0.00186849 | nan                                                   |     -17.9294 |      -17.6571 |


#obtain average coefficent for each feature
df = pd.DataFrame()
for i in range(10):
    df_ = pd.DataFrame(list(zip(abs(model_score['estimator'][i].coef_), X.columns)),columns = ['Coefficient','Feature'])
    df = pd.concat([df_,df],axis=0)

avg_feat_coef = df.groupby('Feature', as_index=False)['Coefficient'].mean()
avg_feat_coef = avg_feat_coef.sort_values(by='Coefficient',ascending=False)


top_10_features = avg_feat_coef.head(10)

plt.style.use('ggplot')
plt.barh(top_10_features['Feature'],top_10_features['Coefficient'])
plt.title('Top 10 Features in Elastic Net CV Model')
plt.ylabel('Feature')
plt.xlabel('Coefficient Value')
plt.yticks(rotation=30, va='top')
plt.show()

	number_of_elements	mean_atomic_mass	wtd_mean_atomic_mass	gmean_atomic_mass	wtd_gmean_atomic_mass	entropy_atomic_mass	wtd_entropy_atomic_mass	range_atomic_mass	wtd_range_atomic_mass	std_atomic_mass	wtd_std_atomic_mass	mean_fie	wtd_mean_fie	gmean_fie	wtd_gmean_fie	entropy_fie	wtd_entropy_fie	range_fie	wtd_range_fie	std_fie	wtd_std_fie	mean_atomic_radius	wtd_mean_atomic_radius	gmean_atomic_radius	wtd_gmean_atomic_radius	entropy_atomic_radius	wtd_entropy_atomic_radius	range_atomic_radius	wtd_range_atomic_radius	std_atomic_radius	wtd_std_atomic_radius	mean_Density	wtd_mean_Density	gmean_Density	wtd_gmean_Density	entropy_Density	wtd_entropy_Density	range_Density	wtd_range_Density	std_Density	wtd_std_Density	mean_ElectronAffinity	wtd_mean_ElectronAffinity	gmean_ElectronAffinity	wtd_gmean_ElectronAffinity	entropy_ElectronAffinity	wtd_entropy_ElectronAffinity	range_ElectronAffinity	wtd_range_ElectronAffinity	std_ElectronAffinity	wtd_std_ElectronAffinity	mean_FusionHeat	wtd_mean_FusionHeat	gmean_FusionHeat	wtd_gmean_FusionHeat	entropy_FusionHeat	wtd_entropy_FusionHeat	range_FusionHeat	wtd_range_FusionHeat	std_FusionHeat	wtd_std_FusionHeat	mean_ThermalConductivity	wtd_mean_ThermalConductivity	gmean_ThermalConductivity	wtd_gmean_ThermalConductivity	entropy_ThermalConductivity	wtd_entropy_ThermalConductivity	range_ThermalConductivity	wtd_range_ThermalConductivity	std_ThermalConductivity	wtd_std_ThermalConductivity	mean_Valence	wtd_mean_Valence	gmean_Valence	wtd_gmean_Valence	entropy_Valence	wtd_entropy_Valence	range_Valence	wtd_range_Valence	std_Valence	wtd_std_Valence	critical_temp
0	4	88.944468	57.862692	66.361592	36.116612	1.181795	1.062396	122.90607	31.794921	51.968828	53.622535	775.425	1010.268571	718.152900	938.016780	1.305967	0.791488	810.6	735.985714	323.811808	355.562967	160.25	105.514286	136.126003	84.528423	1.259244	1.207040	205	42.914286	75.237540	69.235569	4654.35725	2961.502286	724.953211	53.543811	1.033129	0.814598	8958.571	1579.583429	3306.162897	3572.596624	81.8375	111.727143	60.123179	99.414682	1.159687	0.787382	127.05	80.987143	51.433712	42.558396	6.9055	3.846857	3.479475	1.040986	1.088575	0.994998	12.878	1.744571	4.599064	4.666920	107.756645	61.015189	7.062488	0.621979	0.308148	0.262848	399.97342	57.127669	168.854244	138.517163	2.25	2.257143	2.213364	2.219783	1.368922	1.066221	1	1.085714	0.433013	0.437059	29.0
1	5	92.729214	58.518416	73.132787	36.396602	1.449309	1.057755	122.90607	36.161939	47.094633	53.979870	766.440	1010.612857	720.605511	938.745413	1.544145	0.807078	810.6	743.164286	290.183029	354.963511	161.20	104.971429	141.465215	84.370167	1.508328	1.204115	205	50.571429	67.321319	68.008817	5821.48580	3021.016571	1237.095080	54.095718	1.314442	0.914802	10488.571	1667.383429	3767.403176	3632.649185	90.8900	112.316429	69.833315	101.166398	1.427997	0.838666	127.05	81.207857	49.438167	41.667621	7.7844	3.796857	4.403790	1.035251	1.374977	1.073094	12.878	1.595714	4.473363	4.603000	172.205316	61.372331	16.064228	0.619735	0.847404	0.567706	429.97342	51.413383	198.554600	139.630922	2.00	2.257143	1.888175	2.210679	1.557113	1.047221	2	1.128571	0.632456	0.468606	26.0
2	4	88.944468	57.885242	66.361592	36.122509	1.181795	0.975980	122.90607	35.741099	51.968828	53.656268	775.425	1010.820000	718.152900	939.009036	1.305967	0.773620	810.6	743.164286	323.811808	354.804183	160.25	104.685714	136.126003	84.214573	1.259244	1.132547	205	49.314286	75.237540	67.797712	4654.35725	2999.159429	724.953211	53.974022	1.033129	0.760305	8958.571	1667.383429	3306.162897	3592.019281	81.8375	112.213571	60.123179	101.082152	1.159687	0.786007	127.05	81.207857	51.433712	41.639878	6.9055	3.822571	3.479475	1.037439	1.088575	0.927479	12.878	1.757143	4.599064	4.649635	107.756645	60.943760	7.062488	0.619095	0.308148	0.250477	399.97342	57.127669	168.854244	138.540613	2.25	2.271429	2.213364	2.232679	1.368922	1.029175	1	1.114286	0.433013	0.444697	19.0
3	4	88.944468	57.873967	66.361592	36.119560	1.181795	1.022291	122.90607	33.768010	51.968828	53.639405	775.425	1010.544286	718.152900	938.512777	1.305967	0.783207	810.6	739.575000	323.811808	355.183884	160.25	105.100000	136.126003	84.371352	1.259244	1.173033	205	46.114286	75.237540	68.521665	4654.35725	2980.330857	724.953211	53.758486	1.033129	0.788889	8958.571	1623.483429	3306.162897	3582.370597	81.8375	111.970357	60.123179	100.244950	1.159687	0.786900	127.05	81.097500	51.433712	42.102344	6.9055	3.834714	3.479475	1.039211	1.088575	0.964031	12.878	1.744571	4.599064	4.658301	107.756645	60.979474	7.062488	0.620535	0.308148	0.257045	399.97342	57.127669	168.854244	138.528893	2.25	2.264286	2.213364	2.226222	1.368922	1.048834	1	1.100000	0.433013	0.440952	22.0
4	4	88.944468	57.840143	66.361592	36.110716	1.181795	1.129224	122.90607	27.848743	51.968828	53.588771	775.425	1009.717143	718.152900	937.025573	1.305967	0.805230	810.6	728.807143	323.811808	356.319281	160.25	106.342857	136.126003	84.843442	1.259244	1.261194	205	36.514286	75.237540	70.634448	4654.35725	2923.845143	724.953211	53.117029	1.033129	0.859811	8958.571	1491.783429	3306.162897	3552.668664	81.8375	111.240714	60.123179	97.774719	1.159687	0.787396	127.05	80.766429	51.433712	43.452059	6.9055	3.871143	3.479475	1.044545	1.088575	1.044970	12.878	1.744571	4.599064	4.684014	107.756645	61.086617	7.062488	0.624878	0.308148	0.272820	399.97342	57.127669	168.854244	138.493671	2.25	2.242857	2.213364	2.206963	1.368922	1.096052	1	1.057143	0.433013	0.428809	23.0

	number_of_elements	mean_atomic_mass	wtd_mean_atomic_mass	gmean_atomic_mass	wtd_gmean_atomic_mass	entropy_atomic_mass	wtd_entropy_atomic_mass	range_atomic_mass	wtd_range_atomic_mass	std_atomic_mass	wtd_std_atomic_mass	mean_fie	wtd_mean_fie	gmean_fie	wtd_gmean_fie	entropy_fie	wtd_entropy_fie	range_fie	wtd_range_fie	std_fie	wtd_std_fie	mean_atomic_radius	wtd_mean_atomic_radius	gmean_atomic_radius	wtd_gmean_atomic_radius	entropy_atomic_radius	wtd_entropy_atomic_radius	range_atomic_radius	wtd_range_atomic_radius	std_atomic_radius	wtd_std_atomic_radius	mean_Density	wtd_mean_Density	gmean_Density	wtd_gmean_Density	entropy_Density	wtd_entropy_Density	range_Density	wtd_range_Density	std_Density	wtd_std_Density	mean_ElectronAffinity	wtd_mean_ElectronAffinity	gmean_ElectronAffinity	wtd_gmean_ElectronAffinity	entropy_ElectronAffinity	wtd_entropy_ElectronAffinity	range_ElectronAffinity	wtd_range_ElectronAffinity	std_ElectronAffinity	wtd_std_ElectronAffinity	mean_FusionHeat	wtd_mean_FusionHeat	gmean_FusionHeat	wtd_gmean_FusionHeat	entropy_FusionHeat	wtd_entropy_FusionHeat	range_FusionHeat	wtd_range_FusionHeat	std_FusionHeat	wtd_std_FusionHeat	mean_ThermalConductivity	wtd_mean_ThermalConductivity	gmean_ThermalConductivity	wtd_gmean_ThermalConductivity	entropy_ThermalConductivity	wtd_entropy_ThermalConductivity	range_ThermalConductivity	wtd_range_ThermalConductivity	std_ThermalConductivity	wtd_std_ThermalConductivity	mean_Valence	wtd_mean_Valence	gmean_Valence	wtd_gmean_Valence	entropy_Valence	wtd_entropy_Valence	range_Valence	wtd_range_Valence	std_Valence	wtd_std_Valence	critical_temp	H	He	Li	Be	B	C	N	O	F	Ne	Na	Mg	Al	Si	P	S	Cl	Ar	K	Ca	Sc	Ti	V	Cr	Mn	Fe	Co	Ni	Cu	Zn	Ga	Ge	As	Se	Br	Kr	Rb	Sr	Y	Zr	Nb	Mo	Tc	Ru	Rh	Pd	Ag	Cd	In	Sn	Sb	Te	I	Xe	Cs	Ba	La	Ce	Pr	Nd	Pm	Sm	Eu	Gd	Tb	Dy	Ho	Er	Tm	Yb	Lu	Hf	Ta	W	Re	Os	Ir	Pt	Au	Hg	Tl	Pb	Bi	Po	At	Rn
count	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.0	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.0	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.0	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.0	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.0	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.0	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.000000	21263.0	21263.0	21263.0
mean	4.115224	87.557631	72.988310	71.290627	58.539916	1.165608	1.063884	115.601251	33.225218	44.391893	41.448045	769.614748	870.442317	737.474751	832.769649	1.299172	0.926726	572.222612	483.517264	215.631279	224.050033	157.983101	134.720039	144.448738	120.989330	1.267756	1.131138	139.325025	51.369885	51.601267	52.340465	6111.465214	5267.188547	3460.692235	3117.241110	1.072425	0.856037	8665.438818	2902.736814	3416.910784	3319.170628	76.879751	92.717486	54.359502	72.416225	1.070250	0.770757	120.730514	59.332637	48.912207	44.409356	14.296113	13.848001	10.136977	10.141161	1.093343	0.914065	21.138994	8.218528	8.323333	7.717576	89.706911	81.549080	29.841727	27.308061	0.727630	0.539991	250.893443	62.033066	98.943993	96.234051	3.198228	3.153127	3.056536	3.055885	1.295682	1.052841	2.041010	1.483007	0.839342	0.673987	34.421219	0.017685	0.0	0.012125	0.034638	0.142594	0.384968	0.013284	3.009129	0.014874	0.0	0.008892	0.026772	0.061678	0.189889	0.028143	0.106246	0.009050	0.0	0.016042	0.258347	0.010919	0.156817	0.224782	0.006119	0.003191	0.153182	0.035323	0.090182	1.276751	0.014034	0.073997	0.082556	0.155197	0.078662	0.003940	0.0	0.007799	0.326909	0.177556	0.370901	0.442349	0.146367	0.002291	0.055325	0.068072	0.085034	0.007834	0.009152	0.049468	0.120994	0.101269	0.040491	0.004744	0.0	0.004129	0.568440	0.264953	0.030662	0.041494	0.039666	0.0	0.021992	0.017821	0.023959	0.002857	0.009536	0.008832	0.014217	0.008909	0.012716	0.026849	0.009168	0.036086	0.010424	0.038206	0.022512	0.061558	0.034108	0.020535	0.036663	0.047954	0.042461	0.201009	0.0	0.0	0.0
std	1.439295	29.676497	33.490406	31.030272	36.651067	0.364930	0.401423	54.626887	26.967752	20.035430	19.983544	87.488694	143.278200	78.327275	119.772520	0.381935	0.334018	309.614442	224.042874	109.966774	127.927104	20.147288	28.801567	22.090958	35.837843	0.375411	0.407159	67.272228	35.019356	22.898396	25.294524	2846.785185	3221.314506	3703.256370	3975.122587	0.342356	0.319761	4097.126831	2398.471020	1673.624915	1611.799629	27.701890	32.276387	29.007425	31.648444	0.343391	0.285986	58.700327	28.620409	21.740521	20.429293	11.300188	14.279335	10.065901	13.134007	0.375932	0.370125	20.370620	11.414066	8.671651	7.288239	38.517485	45.519256	34.059581	40.191150	0.325976	0.318248	158.703557	43.123317	60.143272	63.710355	1.044611	1.191249	1.046257	1.174815	0.393155	0.380291	1.242345	0.978176	0.484676	0.455580	34.254362	0.267220	0.0	0.129552	0.848541	1.044486	4.408032	0.150427	3.811649	0.132119	0.0	0.101685	0.271606	1.126254	2.217277	0.466710	0.760821	0.119717	0.0	0.138187	0.902732	0.185651	2.728139	3.407763	0.254272	0.129449	0.713075	0.580672	0.982521	2.079375	0.403316	1.115005	1.021279	1.076049	0.676294	0.083907	0.0	0.121254	0.763625	0.429953	4.846459	4.848246	2.084302	0.064728	0.770327	1.005898	1.554018	0.167831	0.688729	0.521820	1.886951	1.839020	0.718043	0.088480	0.0	0.077676	0.983288	2.320822	0.173147	1.282059	0.224657	0.0	0.183173	0.151433	0.155860	0.064737	0.104153	0.098728	0.131417	0.130455	0.214806	0.276861	0.208969	0.851380	0.164628	1.177476	0.282265	0.864859	0.307888	0.717975	0.205846	0.272298	0.274365	0.655927	0.0	0.0	0.0
min	1.000000	6.941000	6.423452	5.320573	1.960849	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	375.500000	375.500000	375.500000	375.500000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	48.000000	48.000000	48.000000	48.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	1.429000	1.429000	1.429000	0.686245	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	1.500000	1.500000	1.500000	1.500000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.222000	0.222000	0.222000	0.222000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.026580	0.026580	0.026580	0.022952	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	1.000000	1.000000	1.000000	1.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000210	0.000000	0.0	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.0	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.0	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.0	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.0	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.0	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.0	0.0	0.0
25%	3.000000	72.458076	52.143839	58.041225	35.248990	0.966676	0.775363	78.512902	16.824174	32.890369	28.539377	723.740000	738.946339	692.541331	720.108284	1.085871	0.753757	262.400000	291.088889	114.135763	92.994286	149.333333	112.127359	133.542493	89.210097	1.066389	0.852181	80.000000	28.598137	35.112518	32.016958	4513.500000	2999.158291	883.117278	66.746836	0.913959	0.688693	6648.000000	1656.847429	2819.497063	2564.342926	62.090000	73.350000	33.700512	50.772124	0.890589	0.660662	86.700000	34.036000	38.372410	33.440123	7.588667	5.033407	4.109978	1.322127	0.833333	0.672732	12.878000	2.329309	4.261340	4.603491	61.000000	54.180953	8.339818	1.087284	0.457810	0.250677	86.382000	29.349419	37.933172	31.985437	2.333333	2.116732	2.279705	2.091251	1.060857	0.775678	1.000000	0.921454	0.451754	0.306892	5.365000	0.000000	0.0	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.0	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.0	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.0	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.0	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.0	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.0	0.0	0.0
50%	4.000000	84.922750	60.696571	66.361592	39.918385	1.199541	1.146783	122.906070	26.636008	45.123500	44.285984	764.900000	889.966667	727.960610	856.202765	1.356236	0.916843	764.100000	510.440000	266.373871	258.449503	160.250000	125.970297	142.807563	113.181369	1.330735	1.242878	171.000000	43.000000	58.663106	59.932929	5329.085800	4303.421500	1339.974702	1515.364631	1.090610	0.882747	8958.571000	2082.956581	3301.890502	3625.631828	73.100000	102.856863	51.470113	73.173958	1.138284	0.781205	127.050000	71.156250	51.125720	48.029866	9.304400	8.330667	5.253498	4.929787	1.112098	0.994998	12.878000	3.436400	4.948155	5.500675	96.504430	73.333333	14.287643	6.096120	0.738694	0.545783	399.795000	56.556240	135.762089	113.556983	2.833333	2.618182	2.615321	2.434057	1.368922	1.166532	2.000000	1.063077	0.800000	0.500000	20.000000	0.000000	0.0	0.000000	0.000000	0.000000	0.000000	0.000000	1.000000	0.000000	0.0	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.0	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.900000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.0	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.0	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.0	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.0	0.0	0.0
75%	5.000000	100.404410	86.103540	78.116681	73.113234	1.444537	1.359418	154.119320	38.356908	59.322812	53.629284	796.320000	1004.117384	765.715174	937.575826	1.551120	1.061750	810.600000	690.703310	297.724924	342.656991	169.857143	158.265231	155.938199	150.988640	1.512348	1.425684	205.000000	60.224491	69.424491	73.777278	6728.000000	6416.333333	5794.965188	5766.015191	1.323930	1.080939	9778.571000	3409.026316	4004.273231	3959.191394	85.504167	110.738462	67.505900	89.975670	1.345894	0.877541	138.630000	76.706965	56.221787	53.320838	17.114444	18.514286	13.600037	16.428652	1.378110	1.157379	23.200000	10.498780	9.041230	8.017581	111.005316	99.062911	42.371302	47.308041	0.962218	0.777353	399.973420	91.869245	153.806272	162.711144	4.000000	4.026201	3.727919	3.914868	1.589027	1.330801	3.000000	1.918400	1.200000	1.020436	63.000000	0.000000	0.0	0.000000	0.000000	0.000000	0.000000	0.000000	6.800000	0.000000	0.0	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.0	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	2.815000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.0	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.0	0.000000	1.350000	0.000000	0.000000	0.000000	0.000000	0.0	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.0	0.0	0.0
max	9.000000	208.980400	208.980400	208.980400	208.980400	1.983797	1.958203	207.972460	205.589910	101.019700	101.019700	1313.100000	1348.028986	1313.100000	1327.593381	2.157777	2.038560	1304.500000	1251.855072	499.671949	479.162305	298.000000	298.000000	298.000000	298.000000	2.141961	1.903748	256.000000	240.164344	115.500000	97.140711	22590.000000	22590.000000	22590.000000	22590.000000	1.954297	1.703420	22588.571000	22434.160000	10724.374500	10410.932005	326.100000	326.100000	326.100000	326.100000	1.767732	1.675400	349.000000	218.696600	162.895331	169.075862	105.000000	105.000000	105.000000	105.000000	2.034410	1.747165	104.778000	102.675000	51.635000	51.680482	332.500000	406.960000	317.883627	376.032878	1.633977	1.612989	429.974170	401.440000	214.986150	213.300452	7.000000	7.000000	7.000000	7.000000	2.141963	1.949739	6.000000	6.992200	3.000000	3.000000	185.000000	14.000000	0.0	3.000000	40.000000	105.000000	120.000000	12.800000	66.000000	4.000000	0.0	4.000000	12.000000	99.925000	100.000000	20.000000	15.000000	3.000000	0.0	3.300000	24.000000	5.000000	75.000000	79.500000	34.900000	14.000000	30.000000	35.380000	45.000000	98.000000	20.000000	41.000000	46.000000	18.000000	19.000000	5.000000	0.0	4.000000	16.700000	9.000000	96.710000	99.976000	99.992000	6.000000	64.000000	45.000000	50.997450	7.000000	99.995000	31.500000	99.200000	83.500000	66.700000	4.000000	0.0	3.000000	24.000000	98.000000	4.998000	185.000000	6.000000	0.0	12.000000	6.000000	4.000000	5.000000	5.000000	5.000000	5.000000	5.000000	16.000000	7.000000	25.000000	55.000000	14.000000	97.240000	10.000000	45.000000	5.800000	64.000000	8.000000	7.000000	19.000000	14.000000	0.0	0.0	0.0

	O	Cu	Ag	Ba	La	critical_temp	material
0	4.0	1.0	0.0	0.20	1.80	29.0	Ba0.2La1.8Cu1O4
1	4.0	0.9	0.1	0.10	1.90	26.0	Ba0.1La1.9Ag0.1Cu0.9O4
2	4.0	1.0	0.0	0.10	1.90	19.0	Ba0.1La1.9Cu1O4
3	4.0	1.0	0.0	0.15	1.85	22.0	Ba0.15La1.85Cu1O4
4	4.0	1.0	0.0	0.30	1.70	23.0	Ba0.3La1.7Cu1O4

Begin Modeling¶